A minimal mathematical model of calcium homeostasis
Catherine
Lloyd
Auckland Bioengineering Institute, The University of Auckland
Model Status
This CellML model runs in both OpenCell and COR but unfortunately it does not replicate the published results. The units have been checked and they are consistent. Several parameter values were missing from the model description in the original paper. Where a value for a variable is unknown it has been defined as 1.000 in this CellML model (these added values are distinct from any value which is definitely known to be 1 by including 3 decimal places).
Model Structure
ABSTRACT: A mathematical model of calcium homeostasis is presented in which the controlling factors are the plasma concentrations of calcium, PTH, and calcitriol, and the effector organs are the parathyroids, bone, kidney, and intestine. Other factors can be added as the need arises. The model is aimed at simulating what happens in a single individual, but its parameters and variables were adjusted to the corresponding published average values. Simulations of published observations in humans undergoing the infusion of calcium or its chelators are presented. With a single exception, these simulations provided a good fit to the data. The response of the system to extrinsic perturbations was characterized by simulating chronic infusions of calcium, PTH, and calcitriol. Finally, the steady state response to perturbations in some of its parameters (the secretory mass of the parathyroids and the affinity and/or sensitivity of the calcium, PTH, and calcitriol receptors) and to renal failure were also investigated in an attempt to analyze the pathogenesis of clinical hypo- or hypercalcemias. In its present form the model cannot be used to base clinical decisions in individual cases. However, it requires modest computational resources, and clinicians with a modest mathematical background can manipulate it. It is a useful tool for the analysis of general mechanisms of the diseases of calcium metabolism and for the design of clinical experiments aimed at characterizing these diseases. The model can also be the core of future autoadaptive extensions to be used in individual patients.
model diagram
Block diagram of calcium homeostasis. Arrows represent the equations of the model; solid lines are feed forward actions; dashed lines are feedback loops; dotted lines are calcium and phosphate millimole_per_hours; shaded rounded rectangles are pools; open rounded rectangles are target organs; open rectangles are relevant quantities; crossed circle represents an instantaneous difference between phosphate intake and phosphate excretion; starred blocks are pools introduced to produce adjustable delays; triple arrow represents coupling between calcium and phosphate millimole_per_hours in and out of the bone.
The original paper reference is cited below:
A minimal mathematical model of calcium homeostasis, Raposo JF, Sobrinho LG, Ferreira HG, 2002, The Journal of Clinical Endocrinology and Metabolism, 87, 4330-4340. PubMed ID: 12213894
Q_Ca_p
calcium pool
Q_P_p
phosphate pool
Q_P_c
intracellular phosphate
Q_PTH_p
PTH pool
Q_Ca_b
exchangeable pool of calcium in the bone
Q_P_b
exchangeable pool of phosphate in the bone
Q_E_k
1-alpha-hydroxylase in the kidney
Q_D_p
calcitriol in the extracellular fluid compartment
Q_TCa_i
calcitriol-dependent intestinal calcium transport pool
Q_C_PT
secretory mass of the parathyroid gland
Q_TP_k
external balance-dependent phosphate kidney transport pool
Lloyd
Catherine
May
c.lloyd@auckland.ac.nz
The University of Auckland
Auckland Bioengineering Institute
keyword
calcium dynamics
phosphate
bone
parathyroid hormone
endocrine
12213894
Raposo
J
F
Sobrinho
L
G
Ferreira
H
G
A minimal mathematical model of calcium homeostasis
2002-09
The Journal of Clinical Endocrinology and Metabolism
87
4330
4340